We are interested in the weak limit as \(N\rightarrow \infty \)  of \(\left(^{(N,n)}_t\right)_{t\ge 0}\) .
The correct time scale for \(\left(^{(N,n)}_t\right)_{t\ge 0}\) , as is for Cannings' models,
is given by the probability \(c_N= \frac{1}{N(N-1)}\sum _{i=1}^N \mathbb {E}\left[\xi _{i,N}\left(\xi _{i,N}-1\right)\right]\) 
that two randomly chosen individuals have the same parent in the previous generation.
We now introduce some additional notation. Let \({P}_{[0,1]}\)  be the space of mass partitions endowed with the \(\mathsf {L}^{\infty }\)  topology,
and consider a \(\Xi \) -coagulation measure on \({P}_{[0,1]}\)  (see Section 4.2.4 in [1]}). We let
\({Q}_{\Xi ,n}(\cdot ,\cdot )\equiv {Q}(\cdot ,\cdot )\)  to be the coagulation matrix of the
\(\Xi \) -coalescent with values on \({P}_{n}\) , and also set
\({Q}_{\Xi ,n}(\tilde{\pi })\equiv {Q}(\tilde{\pi }){Q}(\mathbf {0}_n,\tilde{\pi })\) .
